7th Grade Solving Two-Step Equations Test Solutions and Scoring (PDF)

7th Grade math test solutions: Solving Two-Step Equations – Maths PDF

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This two step equations test answers for 7th Grade covers solving two-step equations (Common Core 7.EE.B.4a), with a free PDF to print.

Use this answer key and scoring guide to grade the two-step equations test. Each solution shows the full work, and the scoring note explains how the points are awarded. Give partial credit for correct steps even when the final answer is wrong.

Grade 7 · Common Core State Standards: 7.EE.B.4a

Two step equations test answers: worked solutions

Question 1 – Two-step [2 pts]

Add $9$ to both sides: $6x=42$

Divide both sides by $6$: $x=7$

Check: $6(7)-9=33$

$x=7$

Scoring: 1 point for the first correct inverse step; 1 point for the solution and check.

Question 2 – Parentheses [2 pts]

Divide both sides by $-4$: $x+5=7$

Subtract $5$ from both sides: $x=2$

Check: $-4(2+5)=-28$

$x=2$

Scoring: 1 point for the first correct inverse step; 1 point for the solution and check.

Question 3 – Fractions [2 pts]

Subtract $\frac{1}{2}$ from both sides: $\frac{3}{4}x=5$

Divide both sides by $\frac{3}{4}$: $x=\frac{20}{3}$

Check: $\frac{3}{4}(\frac{20}{3})+\frac{1}{2}=\frac{11}{2}$

$x=\frac{20}{3}$

Scoring: 1 point for the first correct inverse step; 1 point for the solution and check.

Question 4 – Decimals [2 pts]

Add $2.4$ to both sides: $1.5x=9$

Divide both sides by $1.5$: $x=6$

Check: $1.5(6)-2.4=6.6$

$x=6$

Scoring: 1 point for the first correct inverse step; 1 point for the solution and check.

Question 5 – Write and solve [2 pts]

$2t+12=46$, so $2t=34$ and $t=17$.

$17 per ticket

After the fee, two tickets share $34.

Scoring: 1 point for the equation; 1 point for the solution.

Question 6 – Two methods [2 pts]

(a) $26-5=21$, $21\div 3=7$.

(b) $3n+5=26$, $3n=21$, $n=7$.

Scoring: 1 point for each method.

Question 7 – Find the error [2 pts]

Liam did not divide the 12 by 3.

$x-2=4$, so $x=6$. Check: $3(6-2)=12$

$x=6$

Scoring: 1 point for the explanation; 1 point for the correct solution.

Question 8 – Kayak rental [3 pts]

Per hour: $(55-25)\div 2=15$. Starting fee $25.
$C=15h+25$
$15h+25=205$, $15h=180$, $h=12$ hours.

More rental hours.

Scoring: 1 point for each part.

Question 9 – Triangle [3 pts]

$x+(x+4)+10=38$, or $2x+14=38$.
$2x=24$, $x=12$.
The sides are 12, 16, and 10, so the longest is 16 inches.

Scoring: 1 point for each part.

Total score

Total

20 points

Key facts behind this two step equations test answers

Key facts

Two forms: $px + q = r$ and $p(x + q) = r$.
Undo addition or subtraction first, then multiplication or division.
Do the same operation to both sides.
Fractions and decimals follow the same steps as whole numbers.
Check by substituting the solution into the original equation.

How to use this two step equations test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 7 chapters: Grade 7 math.

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